Proposed Exercises:

How
many different coin combinations could a person have if she has
exactly 21 cents?

In
the movie Tandem, a character explains that the number on his
car's odometer, 83238, is a palindrome, since it reads the same from
left to right as from right to left. He then remarks that the next
palindrome will be 83338. What number is the seventh palindrome after
83338?

The
pattern AABBBCCCCAABBBCCCC continuously repeats. What is the 2003rd
letter in the pattern?

Without
using a calculator or computer, determine which is larger, 23000
or 32000.

If
a and b are positive integers, neither of which is
divisible by 10, and if ab = 10,000, find the sum a + b.